Geometry for pivot tonearms - calculation errors??

During several threads in Audiogon's Analog forum the question of pivot tonearm geometry was discussed widely and wildly the past weeks. There seems to be a great confusion about the interelation - and interaction - between overhang, offset, effective length, mounting distance and the position of the 2 zero-error points on the arc over the LP's grooved area.
However - the correct tonearm geometry is paramount for the performance of any analog sourced High-end system.

Do we need a new calculation of these parameters?
Is mounting distance a variable factor in a given pivot tonearms geometry?
Can overhang serve as the fixed parameter for a pivot tonearm?
Is effective length a variable or a fixed parameter in pivot tonearm geometry?
Is there anything like an optimum geometry for a given cartridge/pivot tonearm set-up?

I invite all interested in this complex and very important topic to contribute their thoughts. If possible please do include the geometrical derivation for any given theory and opinion.
This might be difficult in some examples, but please try.
By doing so, - this will keep this thread on terms and will make it more valueable for all.
Wow-you need to spend more time at VA. This stuff has been widely discussed, and thanks to some kindly VA members virtually anyone willing to put in a little study can be an alignment expert. But here's a good start:

John Elison has an excel spread sheet that allows you to extrapolate null points for any pivot-to-spindle and effective tonearm length for both Lofgren A (Baerwald) and Lofgren B. The link below gives you instructions, and there is a link at the bottom of that page to the actual Excel file. (BTW, JE's on a crusade to call Baerwald 'Lofgren A', since his studies have shown that Lofgren published an identical geometry long before Baerwald)

Conrad Hoffman (old nuff 2 no better) has produced an arc protractor calculator that allows you to input custom spindle-to-pivot lengths, null points, etc. to print out an arc protractor of your own design. A boon for those of us with several makes of tonearms, and it's fun exploring differing alignment configurations (it has inputs for Lofgren A (Baerwald), Lofgren B, and Stevenson) to determine which alignment you prefer. For you Mint, or other custom, protractor buyers, this will allow you to dictate to the custom builder the parameters that *you* enjoy, from actual experience.

Then, of course, there's the great Cartridge Data Base produced by 'EdAInWestOC' that has a wealth of data on specific cartridges, along with a calculator to allow you to match your cart's compliance and mass to an arm with the correct effective mass. Thanks again Ed for all your hard work.

Plus, the Vinyl Engine has several good articles exploring pivot tonearm geometry, and searching the archives at VA will provide a great deal of discussion and added knowledge. But the three links above make the whole deal so, so much easier.
Dear John: Good to see your links, by coincidence ( in other thread: ) I posted your first link ( calculator ) that is very useful.

Well, this is an interesting one too:

Through these links and many others almost all of us can/could make and try different " options " on the subject and decide which " distortions " likes more to each one of us or which " distortions " match our music/sound quality performance reproduction in our home audio systems. Even we can create " new " tonearm geometry equations.

Dertonarm, about your questions there are different answers depending on the approach you take, in my case I don't want to " invent " something new but to optimize what we have already in hand.
Something that I learn through the time ( experiences ) and through our self tonearm design is that each time you change the effective length ( by changing the overhang or changing the pivot to spindle distance, etc, etc ) we change the tracking distortions/tracking error.
In a pivot tonearm we can't to be at cero tracking error so IMHO what we have to look for is the best way ( best trade-offs for each one of us ) to put at minimum.

As you point out this is a very complex subject and where ( till today, at least I don't know it ) there is no perfect whole answer.
We have to take in count other very important subjects on the tonearm-cartridge set-up where any deviation on any of those set-up parameters degrade or invalidate our " perfect " efforts.

The analog medium is totally imperfect input to output and the best we can do is try to put at minimum every kind of distortions from " everywhere " source and certainly the tonearm audio item is a critical link in this analog audio chain.

Regards and enjoy the music.
Dear Johnbrown, thanks for the input.
A good start for this thread.
And the above mentioned links are useful indeed.

However - this is all included in the G.F.Dennes Tonearm Analysis and Summary. These are all about the different options in calculating the arc and the position of the 2 zero-points (together with the maxima and minima of the derivation from the zero-track of course).

I nevertheless got the impression during several threads the past weeks that the BASIC tonearm geometry (all the mentioned links are dealing mostly NOT with the basic geometry, but with the alignment of the stylus) is indeed hardly discussed at all.

Otherwise there wouldn't be that much irritation and confusion about the basic geometry of the tonearm itself - mainly spindle - pivot mounting distance and its ealtions to effective length, offset and overhang.

Baerwald, Stevenson, Bauer, Loefgren - this is all about the aligment of the stylus and the different options of the tracking arc over the LP grooved area.

This is not dealing with the basic geometry of a given tonearm but with its geometrical interaction with the mounted cartridge.
Dear Raul, I agree with you - this is a complex subject. What I am aiming here is the difference between the basic tonearm geometry (for the individual tonearm) and the geometry for the interaction with a stylus (Baerwald, Loefgren, Bauer, Stevenson etc etc.).

I would like to have some light here that there are 2 tonearm geometries - NOT one. We need to fix the 1st - then proceed with any of the mentioned options in the 2nd geometry calculation.

Its this basic TONEARM-geometry I am target on.
Raul-thanks, and maybe all the info and links I presented-*in one post*-will help others to start studying the issue.

Dertonarm-Well, for me-I'm no math wizard-the combination of the JE and CH programs allow me to take alignment theory as far as I want to go. When you've got one program that will allow you to manipulate any of the parameters of the pivot-arm geometry, display the null points in graph form, and then show the percentage of distortion of the stylus through that arc, and *then* use the CH program to immediately print out a protractor that displays that alignment-that's as far as I can go. I'll leave it to others smarter than I to come up with 'new' interpretations and methodology for tracing a pivot stylus over an LP. Saying that, I'll keep reading this thread and to see at what you arrive. (-:
Dear Dertonarm: Could you share your " finds " /thoughts n that 1st geometry for we can understand and try to help about?, because both have an intimate relationship.

Regards and enjoy the music.
Dear Raul, - let me put it in a few "axioms":

1) offset, overhang and effective length do relate to each other and CAN be CHANGED WITHOUT changing the PIVOT-BEARING DISTANCE. Offset, overhang and effective length do change when you align to a different arc-calculation (say - change from Baerwald to Loefgren).

2) If you change the pivot-bearing distance you change the WHOLE GEOMETRY of the given tonearm.

3) you usually get the very best results with the recommended pivot-bearing (= mounting distance) as specified by the manufacturer, because the whole geometry of the given tonearm builds on that one parameter.

4) whether you choose Loefgren, Bauer, Baerwald, Stevenson or whatever calculation for the alignment of the stylus (and these calculations are onyl aiming at the position of the stylus - not at the position of the tonearm !!) is INDEPENDENT from the geometry of the tonearm itself. These alignments can all be done at the headshell alone without moving the base (and thus the pivot-bearing distance). And they should be done without moving the base because that way you can be sure that the basic geometry of your given tonearm is as specified by the manufacturer.

I think we must clearly put a line here between the geometry of the tonearm WITHOUT a cartridge.

This is the basic geometry of the tonearm itself = 1st geometry.
This is step 1.
Then there is the geometry of the stylus in a given tonearm = 2nd geometry. This is step 2.
Here we have the option to align to whatever calculation does fit our needs best (for instance more modern pressings with long run-out-grooves or pressings from the early 1960ies with the inner grooves running close to the label - these need different alignments - one rather Loefgren - one rather IEC). Here we lay the position of the 2 zero-error points and the maxima and minima derivation. This 2nd alignment does have variations in the offset, overhang and effective length (not much, but some) - but NOT in the pivot-bearing (mounting) distance.

Thank you for your direct email. I will put together a few "basics"/standards for LP-quality and will email to you in the next 2 days.
Dertonarm, How then do you feel about the SME tonearms, which utilize a sliding pivot point in order to achieve pivot to stylus adjustments? In the process the pivot to bearing or spindle distance is also altered pari passu.
Dear Lewm,
the SME 300 series (including SME V and IV) is one of the very few tonearms which does come with a kind of "fixed" geometry in ALL parameters. Given its unability to adjust offset, overhang (we can just move the base - which we shouldn't... - NOT the cartridge ) and effective length, it surely is a fairly unique sample.

Make no mistake - the SME V was designed for a specific mounting distance spindle to pivot-bearing! The SME sliding base is often mistaken for being an "invitation" to "adjust" the base "freely" to whatever alignment you want.

Not so.

SME does specify a mounting distance of 215.35 mm.
See here:

They did not give this very precise figure out of the blue........

SME took for granted all industry standards of its day (early 1980ies) and said:

"well, if all cartridge designers do obey to and follow the standards given and if all LPs are cut following the new IEC standard, then evrything will be perfect with our new tonearm - it will be the "best tonearm in the world"............"

But the world is an imperfect one and many people do want to go their own ways.

The new SME surely was the LEAST UNIVERSAL tonearm ever designed .......
It is for sure the one tonearm which gives almost no possibilities to adjust to specific cartridge needs or to different arcs.

The SME V was a child of its day and was regarded when introduced as the first tonearm which took all (some of them fairly new...) industry standards for record-cutting and cartridge dimensions serious.
Too serious.

Only a cartridge with 100% orientated cantilever and 100% standard horizontal distance mounting holes-stylus can be correctly aligned in a SME V and can only be aligned to ONE standard cuve/arc - the IEC.

Offset can not be aligned in an SME - thats why the SME template does FORCE the user into one possible geometry only.
Thats why the MINT tractor is so very effective with a SME V and a specific cartridge.

In a biological sense the SME V (and its offsprings with fixed headshell and fixed mounting holes) is the very opposite of evolutionary versatile.
It can not "adjust" to any change in the "enviromental conditions".
With the "right" cartridge, it is a VERY serious tonearm.
But there are so very few "right" (read: 100% following IEC standards) cartridges for the SME V around.......
here me meet again.
Just been thinking about Dear Lewm's input, which makes me think to start a thread for the 'poor' V owners i.e. which carts are a GOOD/BEST fit?

I guess we'd mostly look for MCs despite Raul's most extensive experience in MMs.

The cart stylus to mounting hole distance IEC-standard? is in any case to be 9.5 mm for the V arm.
DerTonarm will want to know it a bit more down to the 100th mm so we'll call it 9.52 mm (actually 5/8"). Now for me that begs the question why ICE would have settled for inches?! The mounting hole distance of 1/2" is also not quite metric, now is it?

What do you think? There'd be some folk to give some best fit input?
I use a Windfeld as you know --- and I would not add that to the list of BEST FIT! Amen. Sound great, but not BEST FIT in the alignmnet sense, methinks.

What else can a V owner do? You have mentioned all's fixed, can't even mess around with different flavours A, B, Stevenson...
It's vanilla SME, or go buy some other tone-arm, right?

Best greetings,
Dear Axel: My experience on cartridges are that: experiences on cartridges, MC or MM. I don't now why I give the impresion that I'm or have a MM bias, I'm not.
I have several MC experiences with vintage and today cartridges ( I own and owned ) and like the MM ones the MC has its own advantages and dis-advantages, same with the MM.

+++++ " With the "right" cartridge, it is a VERY serious tonearm... " +++++

absolutely yes.

Btw, the non-perfect world on the cartridge building is more " delicate " because this audio item is not a " mass production " one but almost made each one by hand where we even find " differences " between cartridges on the same model. So what the " poor " V owners have to do is " wait " to be lucky with the cartridge we have. Of course that are some " things " that we can do but always this " things " are add-ons that ( one way or the other ) could compromise the performance.

Dertonarm, I have too some interesting subjects on the LP " standards ", we keep in touch very soon.

Regards and enjoy the music.
you are one of a dieing breed that STILL knows about MMs! That does in way mean to imply that you ONLY know about that.
But how many folks have gone through a truck load of that MM stuff? Nobody I'll ever know I'm sure, so please see it as a compliment and NOT as a limitation.
Bless you,
PS: so please give me some idea about the Shure V15 on a SME V, now how about that?!
Dear Axel: I mounted my 97Xe ( a small brother of the V15 ) in the IV and works fine so I don't see any trouble with your combination.

I don't like to speak about devices that already own a person but I can't stay " quiet " . This next thoughts/experiences are in the animus to help about:

I owned the V15MR that I try in different tonearms/headshells and with different load impedance values and in my system I never achieve " stellar " or near it quality performance even the 97Xe like me more and that's why I still have it.

If you or any other person wants to " introduce " in the MM high-end " stage " the V15 IMHO is not the right answer if we want to compare against a top LOMC like the one you own.
My advise is to go for one of the next cartridges ( either ): Nagaoka MP-50 or better yet the MP-50 Super, Ortofon M20FL Super, Audio technica ATML180 OCC and/or Signet TK 10MLII.

Anyone of you could be " shocked " with the quality performance on these MM cartridges. Can/could beat a top LOMC ones?, I know the answer but the best judge are you.

Those cartridges are only the tip of the MM iceberg.

Normaly these MM cartridges perform better with a load impedance over 70K and total capacitance below 200pf and are so " inexpensive " that we can own dozens.

No, I'm not saying or implying in anyway that instead of our beloved LOMC ones: no, the MM is another very good " flavored " source.

Regards and enjoy the music.
Dear Axel, dear Raul, - I am very familiar with teh AT-180 ML and I want to support Raul's recommendation of thsi particular cartridge. It is outstanding - a very serious contender for most of the $1k to $3k of todays high-flight MCs.
It should work very good in the SME V as should its bigger brothers from AT - why?
Because all AT-cartridges do very precisely hold on to the standards (as do all Ortofons...)in stylus to mounting hole distance and therefor will support the fixed alignment of the SME V.

But - can we discuss the SME V in particular in an individual thread??

Hey Axel - how about starting a thread about the special situation of the SME V in terms of its geometry and design?

I am sure this will get much attention as the SME V is widely owned and I will gladly support it.
I'll think about it. I'd say it sounds the right idea.
Also, I don't want to 'twist' this thread into the wrong direction.
Thanks for the suggestions.
Dear all, The separation in 'Tonearm Geometry' and 'Setup
Geometry' as proposed by our 'new authority' in tonearm
matter, Herr Dertonarm (sorry Raul) is the subject-matter
of one article in Audio,January 1980. The authors Kessler
and Pisha ware very suprised to discover that the most
Japanese tonearms producer got the 'arm geometry' wrong
(the 'beloved' FR-64 included). Suprised because the so
called ' optimal geometry' was know since,at least,1941.
The math. was my worst subject at school and I am realy
'annoyed' to be confronted with difficult 'formulae' in
my hobby. BTW the '1mm unit' is to me the smallest I can see and handle so I have no idea how to get my stylus 'spot
on' at 66,04 mm and 120,9 mm respectively.
Herr Dertonarm is 'threaten' us with the 'fractions' of
the 'unit' mentioned and call himself a Humanist. To me
he is a direct descendant of Frege (alias 'Perfectionist').
If we intend to get this 'perfect Geometry' in reality
then the chance to end in an psychitric instition is much
much larger then to get this 'TT-tonearm-stylus' conundrum
in correspondance with the 'demands' as stated by this
German perfectionist.

Regards and enjoy the music (if you can)
Dear Nandric, many quote marks indeed........
I am constantly puzzled how many people do react so anoyed if they are confronted with the pursuit for perfection in technical parameters.
As for the FR-64s I have already made enough comments and already gave the correct and optimzed mounting distance.
Anyone NOT interested in getting the tonearm/stylus geometry as close to perfection as possible has a very good option:

in 1982 the - soon to be history again - audio CD was invented.

This was made for all those countless numbers of music connaisseurs whose smallest unit is the 1mm (which is several hundered times larger than the polished contact area of your stylus).

If you try (try....) to get the perfect geometry, you will not end in the asylum, but maybe end up with no distortion in analog playback and just the sonic results the audio press always promised you.

Leave it to try-and-error is certainly not the way to align a mechanical device.

But - sorry to have created pains in your old wounds with math (also I do not really recall having given any formulas regarding tonearm geometry - I was just displaying geometrical aspects.

BTW - Kessler and Pisha weren't all that correct in their article either and had relativeted most of their "findings" in later years.
Dear Dertonarm, My comparition with Frege was not
'accidental'. In intellectual or academic sence you can't
get a greater compliment. But even this 'greatest mind' of
Europe was 'destroyed' by his obsession with 'fundation of
math.';he never recovered from 'paradoxes' of ,say,set-
From Frege I learned not to treat 'disjunction' as 'entweder-oder' (or-or)proposition. So I am very puzzled with your statement:'Anyone NOT interested in
getting the tonearm/stylus geometry as close to perfection
as possible has a very good option: CD'.
Sorry Dertonarm but this statment is senseless to me.
Are you some kind of legislator?
I can assure you that I and others enjoy our 'imperfect'
TT-tonearm-stylys combos even if we know that thy are not
perfect. To me the quality of LP's (I own more then 3000)
is a much greater problem.
So don't get obsessed with 'theoretical matter'.
Dear Nandric, over the last 5 years I have mounted and aligned about 35 High-end and high-priced cartridges including Lyra Olympus, Lyra Titan and Skala, Kondo IO, Dynavector XRV-1s, Koetsu RSP and Coral Stone, Miyabi Takeda - to name just the more prominent and current ones. Tonearms included all FR-60 family, Da Vinci, Kuzma Airline and P4, Graham Phantom, Micro MAX in all incarnations, SME (all...), even Linn Ekos.

So my practical analog life has its place too aside the theoretical matters.......
The owners asked me to align their high-priced items because I am getting outstanding results in tonearm/cartridge set-up. I do so because of extreme care and because I taking all mechanical and dynamical issues into account and know how to handle them. This is a result of digesting all theoretical background, the skill to use it for practical resuklts and a lot of routine over 30 years.
I am not obssesed with theoretical matters, but I have learned to get practical real world results from digesting the theoretical background and putting all analog handwork on a very solid basis.
To math and geometry it makes no difference whether you like them or not (I didn't liked them in school either...) - the question is rather why not use them for good ?
This is no high math - its all fairly simple 2-dimensional geometry. Drawing on a sheet of paper does very likely clarifies many points - and simplifies them too - which may "sound" theoretical and abstract.
However they aren't.
Putting the mechanical foundations straight and clear just helps getting better sound.
Its that simple.
There are enough areas in our music-systems where it is MUCH more difficult to get things straight and to find the path for sonic improvement (I have built many tube amplifiers and preamps - believe me, they sometimes are a pain far beyond any problems in analog front-end).

The anaolg front-end is all mechanic and dynamic interactions.
I find it fascinating, as this is the one area where we can actually "see" whats going on and can have much more direct influence for the better than in any other part of the chain.
Thank you johnbrown and Dertonarm. Good to have more geometry delineation.
Every little bit of knowledge helps out with the puzzle.

Happy (analogue) Listening!